I would not doubt it at all. Korea during this time very much revolved around money and noble blood, so for a common woman (from a fishing village no less, who probably did hard labor before being married to the Emperor) would never be fit in the eyes of the rich nobility.
They (like most and any other noble throughout the world and through history) had tried marrying their daughters to him as consorts, or even concubines after he married Consort Ahn, and he either completely ignores them or just flat out said "No, I'm only marrying her." She was an eyesore for being a commoner and getting in the way of their machinations (almost always more money lol) and so she had to die.